Nonlinear vibration analysis of a generally restrained axially loaded beam structure with a local uniform nonlinear foundation

Beam structures are widely used in various engineering occasions to model various structures. Numerous researchers have studied dynamic responses of beam structures with nonlinear supports or nonlinear foundations. In engineering, nonlinear supports were subjected to the beam structure through the surface contact rather than the point connection. Few works studied the dynamic behavior of the beam structure with local uniform cubic nonlinear stiffness foundations. Additionally, the boundary rotational restraints of the beam structure are ignored. To improve the engineering acceptance of the beam structure with nonlinearity, it is of great significance to study the dynamic behavior of the generally restrained axially loaded beam structure with a local uniform nonlinear foundation. This work establishes a nonlinear dynamic model of the beam structure with a local uniform nonlinear foundation. Dynamic responses of the beam structure are predicted through the Galerkin truncated method. In Galerkin truncated method, mode functions of the axially loaded beam structure without the local uniform nonlinear foundation are selected as the trail and weight functions. The harmonic balance method is employed to verify the correctness of the Galerkin truncated method. The influence of the sweeping ways and local uniform nonlinear foundation on dynamic responses of the generally restrained axially loaded beam structure is investigated. Dynamic responses of the generally restrained axially loaded beam structure with a local uniform nonlinear foundation are sensitive to its calculation initial values. Suitable parameters of the local uniform nonlinear foundation can suppress the vibration response and transform the vibration state of the beam structure.